Question

A particular type of 4th grade Achievement Test provides overall scores that are normally distributed with a mean of 50 and a standard deviation of 10.

What is the probability that a randomly selected student earns a score between 33 and 48?

Answer 1

The probability that a randomly selected student earns a score between 33 and 48 is 0.3761

Explanation:

We compute the z-score related to some value x as
`z=(x-50)/(10)`. The z-score related to 33 is given by
`z_(1)=(33-50)/(10)=-1.7` and the z-score related to 48 is given by
`z_(2)=(48-50)/(10)=-0.2`. Therefore, the probability that a randomly selected student earns a score between 33 and 48 is given by P(-1.7 < Z < -0.2) = P(Z < -0.2) - P(Z < -1.7) = 0.4207 - 0.0446 = 0.3761.